Numerical Methods in Electromagnetic Field Theory I (NFT I)

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Table of Contents:

bulletLecturer
bullet Overview of the Contents
bullet Prerequisites, Time, Units, Language, Exam
bullet References
bullet List of Numerical Methods
bullet Software
bullet Programming Languages and Tools
bullet Lecture Notes
bullet Exercises and Solutions
bullet Programs

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Lecturer

        Dr.-Ing. René Marklein

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Overview of the Contents

Maxwell's equations; Wave equations; Numerical solution of Maxwell's equations; Finite difference method (FDM); Finite difference time domain (FDTD); finite integration technique (FIT); finite element method (FEM); finite volume method (FVM); examples and applications.

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Prerequisites, Time, Units, Language, Exam

Mathematics I/II; Basics of Electrical Engineering I-III; Mathematical Foundation of Electromagnetic Field Theory I/II; Recommended Semester: 5th Semester (regular Students), 1 Semester (Master Students); Winter semester (WS); 2 lecture and 1 exercise; English/German; Oral exam in the winter and summer semester

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References

bulletChew, W. C.: Waves and Fields in Inhomogeneous Media. D. Van Nostrand Reinhold, New York, USA, 1990.
bulletGolub, G., J. M. Ortega [1993], Scientific Computing: An Introduction With Parallel Computing, Academic Press, San Diego, CA, USA. [amazon.de] [amazon.com]
bulletHarrington, R. F.: Field Computation by Moment Methods. IEEE Press, Piscataway, New Jersey, USA, 1993 (Nachdruck der Originalausgabe: R. E. Krieger Pub. Company, Fla., USA, 1968).
bulletKunz, K. S., R. J. Luebbers: Finite Difference Time Domain Method for Electromagnetics. CRC Press, Boca Raton, Florida, USA, 1993.
bulletLangenberg, K. J.: Skript zur Vorlesung: Elektromagnetische Feldtheorie II & III. FG Theoretische Elektrotechnik, FB Elektrotechnik/Informatik, Universität Kassel, Kassel, 2002.
bulletMarklein, R.: Numerische Verfahren zur Modellierung von akustischen, elektromagnetischen, elastischen und piezoelektrischen Wellenausbreitungsproblemen im Zeitbereich basierend auf der Finiten Integrationstechnik. Shaker Verlag, Aachen, 1997.
bulletPeterson, A. F., S. L. Ray, R. Mittra: Computational Methods for Electromagnetics. IEEE Press, Piscataway, New Jersey, USA, 1998.
bulletPress, W. H., S. A. Teukolsky, W. T. Vettering, B. P. Flannery: Numerical Recipes in C: The Art of Scientific Computing. 2nd ed., Cambridge University Press, USA, 1994. [online version] [amazon.de] [amazon.com]
bulletSaad, Y.: Iterative Methods for Sparse Linear Systems. PWS Publishing Company, Boston, USA, 1996.
bulletSmith, G. D.: Numerical Solution of Partial Differential Equations: Finite Difference Method. 3rd ed., Clarendon Press, Oxford, UK, 1985.
bulletStrikwerda, J. C.: Finite Difference Schemes and Partial Differential Equations. Wadsworth & Brooks/Cole, Mathematics Series, Pacific Grove, California, USA, 1989.
bulletSullivan, D. M.: Electromagnetic Simulation Using the FDTD Method. IEEE Press, Piscataway, New Jersey, USA, 2000.
bulletTaflove, A.: Computational Electrodynamics: The Finite-Difference Time-Domain Method. 2nd Ed., Artech House, Norwood, Mass., USA, 2000.
bulletVolakis, J. L., A. Chatterjee, L. C. Kempel: Finite Element Method for Electromagnetic. IEEE Press, Piscataway, New Jersey, USA, 1998.

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List of Numerical Methods

bullet

Finite Difference Method (FDM)

bullet Finite Difference Time Domain (FDTD) Method
bullet Finite Integration Technique (FIT)
bullet Finite Element Method (FEM)               
bullet Finite Volume Method (FVM)
bulletMethod of Moments (MoM)
bulletThe Cell Method

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Finite Difference Method (FDM)

bullet

Basics
bullet

Taylor Series Expansion

bullet

Approximation Error

bulletSolvers
bullet References

    Basics

    References

bulletAmes, W. F. [1977], Numerical Methods for Partial Differential Equations, 2nd ed., Academic Press, San Diego.
bulletSmith, G. D. [1985], Numerical Solution of Partial Differential Equations: Finite Difference Methods, Oxford University Press, New York. [amazon.de]
bulletStrikwerda, J. C. [1989], Finite Difference Schemes and Partial Differential Equations, Wadsworth & Brooks/Cole, Wadsworth, CA, USA. [amazon.de]

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Finite Difference Time Domain (FDTD) Method

bullet

Basics
bullet

Yee's method, Yee's cell

bullet

Taylor Series Expansion, Approximation Error

bullet References
bulletSolvers
bullet Links

    Basics

    References

bulletKunz, K. S., R. Luebbers [1993], The Finite Difference Time Domain Method for Electromagnetics, CRC Press, Boca Raton, FL, USA. [amazon.de]
bullet Taflove, A. [1995], Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House, Boston, MA, USA. [amazon.de]
bulletTaflove, A., S. Hagness [2000], Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed., Artech House, Boston, MA, USA. [amazon.de]
bulletTaflove, A. (ed.) [1998], Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method, Artech House, Boston, MA, USA. [amazon.de]
bulletSullivan, D. [2000], Electromagnetic Simulation Using the FDTD Method, IEEE Press, New York, USA. [amazon.de]

    Links

bulletfdtd.org
bullet Hagness, Prof. Susan C., University of Wisconsin-Madison, Madison, WI, USA.
bullet Taflove, Prof. Allen, Northwestern University, Evanston, IL, USA.

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Finite Integration Technique (FIT)

bullet

Basics
bullet

Dual Cell Complex, and

bullet

Midpoint Rule, Approximation Error

bulletSolvers
bullet References

    Basics

    References

bulletMarklein, R. [1997], Numerical Methods for the Modeling of Acoustic, Electromagnetic, Elastic and Piezoelectric Wave Propagation Problems in the Time Domain Based on the Finite Integration Technique. Shaker Verlag, Aachen, Germany. (in German) (Amazon (Germany) , Shaker Verlag, Aachen (Germany) )  
bulletvan Rienen, U. [2001], Numerical Methods in Computational Electrodynamics, Springer Verlag, Berlin [amazon.de]

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Finite Element Method (FEM)

bullet

Basics

bulletSolvers
bullet References

    Basics

    References

bulletJin, Jianming [1993], The Finite Element Method in Electromagnetics, John Wiley & Sons, New York. [amazon.de]
bulletKost, Arnulf [1994], Numerische Methoden in der Berechnung elektromagnetischer Felder, Springer, Berlin. [amazon.de]
bulletPelosi, G., R. Coccioli, S. Selleri [1998], Quick Finite Elements for Electromagnetic Waves  [homepage][amazon.de]
bulletPeterson, A. F., S. L. Ray, R. Mittra [1997], Computational Methods for Electromagnetics, IEEE, Piscataway. [amazon.de]
bulletReece, A. B., T. W. Preston [2000], Finite Element Methods in Electrical Power Engineering, Oxford University Press, Oxford. [amazon.de]

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Finite Volume Method (FVM)

bullet

Basics

bulletSolvers
bullet References

    Basics

    References

bulletYee, K. S. [1997], The Finite-Difference Time-Domain (FDTD) and the Finite-Volume Time-Domain (FVTD) Methods in Solving Maxwell's Equations, IEEE Trans. Antennas Propagat., Vol. 45, No. 3, March.

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 Software

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ANSYS/Emag (ANSYS)

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ANSYS/Multiphysics (ANSYS)

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CST Microwave Studio (FI Method, CST - Computer Simulation Technology)
bulletCST MICROWAVE STUDIO™ is a specialist tool for the fast and accurate simulation of high frequency problems.
Applications include the expanding areas of: Mobile Communication, Wireless Design (bluetooth), Signal Integrity, and EMC.
Exceptionally user friendly, CST MWS quickly gives you an insight into the EM behavior of your high frequency designs.
CST MWS offers three solvers: The Time Domain Solver, the Eigenmode Solver and a Frequency Domain solver, as well as
options for the import of specific CAD files and the extraction of SPICE parameters.   

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CST Design Studio (FI Method, CST - Computer Simulation Technology)

bullet

FIDELITY (FDTD, Zeland Software)
bullet

FIDELITY is a FDTD (Finite-Difference Time-Domain) based Full-3D EM Simulator for modeling microwave circuits,
components, and antenna, wireless/RF antennas, EMC and EMI structures, and other high-speed and high-frequency circuitry.

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Ensemble (Method of Moments, ANSOFT)
bullet

Ensemble is a planar method-of-moments (MoM) electromagnetic simulation software package that computes S-parameters
 and full-wave fields for microstrip and planar microwave structures including filters, power dividers, and antennas

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HFSS (FE Method, ANSOFT)
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3D finite element analysis electromagnetic simulation software for RF, Wireless, Packaging, and Optoelectronic design

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IE3D (Method of Moments, Zeland Software)
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Planar and 3D Electromagnetic Simulation and Optimization Package

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MAFIA 4 (FI Method, CST - Computer Simulation Technology)

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SuperNEC (Method of Moments, Unified Theory of Diffraction, Poynting)

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XFDTD (FDTD Method, REMCOM Inc)

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 Programming Languages and Tools

bulletC Programming Environment under Win32
bullet Cygwin
bulletFORTRAN
bullet MPI and PVM
bulletMATLAB
bulletGnuplot
bullet XEmacs
bullet Netlib Netlib is a collection of mathematical software, papers, and databases

Programming in C

    References

bulletKernighan, B. W., D. M. Ritchie [1988], The C Programming Language, Prentice Hall. (amazon.com) (amazon.de)

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 Lecture Notes

    If you download the following PowerPoint files (*.ppt) you have to install additional MathType fonts. The MathType fonts can be downloaded from the homepage of Design Science ( English / German).

   List of Lecture Notes

bullet Lecture 1.ppt, 1 Page A4.pdf, 2 Pages A4.pdf (last update 23.11.2005)
bullet Lecture 2.ppt, 1 Page A4.pdf, 2 Pages A4.pdf (last update 23.11.2005)
bullet Lecture 3.ppt, 1 Page A4.pdf, 2 Pages A4.pdf (last update 23.11.2005) 
bullet Lecture 4.ppt, 1 Page A4.pdf, 2 Pages A4.pdf (last update 10.01.2006)
bullet Lecture 5.ppt, 1 Page A4.pdf, 2 Pages A4.pdf (last update 10.01.2006)
bullet Lecture 6.ppt, 1 Page A4.pdf, 2 Pages A4.pdf (last update 17.01.2006)
bullet Lecture 7.ppt, 1 Page A4.pdf, 2 Pages A4.pdf (last update 24.01.2006)
bullet Lecture 8.ppt, 1 Page A4.pdf, 2 Pages A4.pdf (last update 02.02.2006)
bullet Lecture 9.ppt, 1 Page A4.pdf, 2 Pages A4.pdf (last update 03.02.2006)
bullet Lecture10.ppt, 1 Page A4.pdf, 2 Pages A4.pdf (last update 09.02.2006)  (new)
bullet...

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 Exercises and Solutions

   List of Exercises and Solutions

bullet Exercise 1 (last update 08.11.2005)
bullet Exercise1.pdf
bullet Solution1.pdf
bullet Exercise 2 (last update 23.11.2005)
bullet Exercise2.pdf
bullet Solution2.pdf
bullet Exercise 3 (last update 23.11.2005)
bullet Exercise3.pdf

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 Programs

     List of Programs

bullet1D FD Vacuum (MATLAB source code fd1dvac_rcn_poyn.m )
bulletInput parameter for the first run: Nz = 200, Nt = 500, Nz_Source = 100.
bullet2D FD TM Vacuum (MATLAB source code fd2dtmvac_rcn_poyn.m )
bulletInput parameter for the first run: Nz = 200, Nt = 500, Nz_Source = 100.
bullet1D FDTD Vacuum (C source code fdtd1dvac.c, MATLAB source code fdtd1dvac.m )
bulletMATLAB source code to visualize the output files of the C program (fig_1.m, fig_2.m, fig_3.m)
bulletGnuplot input files to visualize the output files of the C program
bulletInput parameter for the first run: Nz = 200, Nt = 500, Nz_Source = 100.
bullet Instructions: The C program fdtd1dvac.c runs the FDTD simulation and generates output files in binary and ascii format of the Ex and Hy field component and the time history of the excitation pulse. These files can be visualize with the provided MATLAB files fig_1.m, fig_2.m, and fig_3.m. The MATLAB program runs the FDTD simulation and visualizes the Ex and Hy field interactively. If you don't have MATLAB, you can use e.g. gnuplot to plot Ex, Hy, and the pulse contained in the ascii output files of the C program.
bullet Figure 1, generated with MATLAB program fig_1.m
bullet Figure 2, generated with MATLAB program fig_2.m
bullet Figure 3, generated with MATLAB program fig_3.m
bullet1D FDTD Vacuum with Absorbing Boundaries (C source code fdtd1dvacab.c, MATLAB source code fdtd1dvacab.m )
bulletMATLAB source code to visualize the output files of the C program (fig_1.m, fig_2.m, fig_3.m)
bulletGnuplot input files to visualize the output files of the C program
bulletInput parameter for the first run: Nz = 200, Nt = 500, Nz_Source = 100.
bullet Instructions: The C program fdtd1dvacab.c runs the FDTD simulation and generates output files in binary and ascii format of the Ex and Hy field component and the time history of the excitation pulse. These files can be visualize with the provided MATLAB files fig_1.m, fig_2.m, and fig_3.m. The MATLAB program runs the FDTD simulation and visualizes the Ex and Hy field interactively. If you don't have MATLAB, you can use e.g. gnuplot to plot Ex, Hy, and the pulse contained in the ascii output files of the C program.
bullet Figure 1, generated with MATLAB program fig_1.m
bullet Figure 2, generated with MATLAB program fig_2.m
bullet Figure 3, generated with MATLAB program fig_3.m
bullet1D FDTD Dielectric with Absorbing Boundaries (C source code fdtd1ddieab.c, MATLAB source code fdtd1ddieab.m )
bulletMATLAB source code to visualize the output files of the C program (fig_1.m, fig_2.m, fig_3.m)
bulletGnuplot input files to visualize the output files of the C program
bulletInput parameter for the first run: Nz = 200, Nt = 500, Nz_Source = 50.
bullet Instructions: The C program fdtd1ddieab.c runs the FDTD simulation and generates output files in binary and ascii format of the Ex and Hy field component and the time history of the excitation pulse. These files can be visualize with the provided MATLAB files fig_1.m, fig_2.m, and fig_3.m. The MATLAB program runs the FDTD simulation and visualizes the Ex and Hy field interactively. If you don't have MATLAB, you can use e.g. gnuplot to plot Ex, Hy, and the pulse contained in the ascii output files of the C program.
bullet Figure 1, generated with MATLAB program fig_1.m
bullet Figure 2, generated with MATLAB program fig_2.m
bullet Figure 3, generated with MATLAB program fig_3.m

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